Evolution at Molecular Resolution

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2 Evolution at Molecular Resolution Peter Schuster Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA EMBO Members Meeting 2014 Heidelberg,

3 Web-Page for further information:

4 Sewall Wright, Sewall Wright The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: D.F.Jones, ed. Int. Proceedings of the Sixth International Congress on Genetics. Vol.1, Ithaca, NY. Sewall Wrights fitness landscape as metaphor for Darwinian evolution

5 +.. wild type a... alternative allele on locus A : : : abcde alternative alleles on all five loci The multiplicity of gene replacements with two alleles on each locus Sewall Wright Surfaces of selective value revisited. American Naturalist 131:

6 Q 5 : the space of binary sequences of chain lenght l = 5

7 Fitness landscapes became experimentally accessible! Protein landscapes: Yuuki Hayashi, Takuyo Aita, Hitoshi Toyota, Yuzuru Husimi, Itaru Urabe, Tetsuya Yomo Experimental rugged fitness landscape in protein sequence space. PLoS One 1:e96. RNA landscapes: Sven Klussman, Ed The aptamer handbook. Wiley-VCh, Weinheim (Bergstraße), DE. Jason N. Pitt, Adrian Ferré-D Amaré Rapid construction of empirical RNA fitness landscapes. Science 330: RNA viruses: Esteban Domingo, Colin R. Parrish, John J. Holland, Eds Origin and evolution of viruses. Second edition. Elesvier, San Diego, CA. Retroviruses: Roger D. Kouyos, Gabriel E. Leventhal, Trevor Hinkley, Mojgan Haddad, Jeannette M. Whitcomb, Christos J. Petropoulos, Sebastian Bonhoeffer Exploring the complexity of the HIV-I fitness landscape. PLoS Genetics 8:e

8 Evolution as a global phenomenon in genotype space

9 The simplified model

10 dx W dt ji j = = Q ji i= 1 n f W i, ji x i n x i= 1 x i j Φ ; = 1, j = 1, 2,, n Φ = n i= 1 f i x i Manfred Eigen fitness landscape Mutation and (correct) replication as parallel chemical reactions M. Eigen Naturwissenschaften 58:465, M. Eigen & P. Schuster Naturwissenschaften 64:541, 65:7 und 65:341

11 quasispecies The error threshold in replication and mutation

12 Selma Gago, Santiago F. Elena, Ricardo Flores, Rafael Sanjuán Extremely high mutation rate of a hammerhead viroid. Science 323:1308. Mutation rate and genome size

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19 single peak landscape step linear landscape Model fitness landscapes I

20 Error threshold on the single peak landscape

21 Thomas Wiehe Model dependency of error thresholds: The role of fitness functions and contrasts between the finite and infinite sites models. Genet. Res. Camb. 69: linear and multiplicative hyperbolic Model fitness landscapes II

22 The linear fitness landscape shows no error threshold

23 AGCUUAACUUAGUCGCU 1 A-U 1 A-G 1 A-C

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25 Rugged fitness landscapes over individual binary sequences with n = 10 realistic landscape ( ) seeds random number ;, 1,2, 0.5 ) ( 2 ) ( ) ( 0 s m j N j f f d f S f s j n n j η η = + =

26 d = 0 d = 0.5 Quasispecies with increasing random scatter d d = Error threshold: Individual sequences n = 10, = 2, s = 491 and d = 0, 0.5,

27 d = 0.5 d = Choice of random scatter: d = 1.0 s = 637 Error threshold on realistic landscapes n = 10, f 0 = 1.1, f n = 1.0, s = 637

28 d = 0.5 d = Choice of random scatter: s = 919 d = 1.0 Error threshold on realistic landscapes n = 10, f 0 = 1.1, f n = 1.0, s = 919

29 Determination of the dominant mutation flow: d = 1, s = 613

30 Determination of the dominant mutation flow: d = 1, s = 919

31 Predictions of the strong quasispecies concept 1. A strong quasispecies is dominated by a clan of mutationally coupled closely related sequences. 2. A four-membered clan consists of the master sequence being the fittest sequence, its fittest one error mutant, the fittest two-error mutant that has to lie in the one-error neighborhood of the fittest one-error mutant, and the fourth sequence completing the mutationally coupled quartet. 3. Strong quasispecies reproduce more efficiently, are stable to mutation, and should be favored by evolution.

32 Motoo Kimura, Motoo Kimura s population genetics of neutral evolution. Evolutionary rate at the molecular level. Nature 217: , The Neutral Theory of Molecular Evolution. Cambridge University Press. Cambridge, UK, 1983.

33 Pairs of neutral sequences in replication networks P. Schuster, J. Swetina Bull. Math. Biol. 50: ) ( ) ( lim = = p x p x p d H = 1 ) (1 1 ) ( lim ) (1 ) ( lim α α α + = + = p x p x p p d H = 2 Random fixation in the sense of Motoo Kimura d H 3 1 ) ( 0,lim ) ( lim or 0 ) ( 1,lim ) ( lim = = = = p x p x p x p x p p p p

34 A fitness landscape including neutrality

35 Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

36 Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

37 Consensus sequences of a quasispecies of two strongly coupled sequences of Hamming distance d H (X i,,x j ) = 1 and 2.

38 Conclusions 1. Realistic fitness landscapes sustain error thresholds. 2. Quasispecies may be centered around clans of sequences with high fitness, which provide evolutionary stability against increasing mutation rates. 3. Pairs of neutral sequences with Hamming distances one or two form clans and are not subjected to Kimura s random selection.

39 Coworkers Ivo L.Hofacker, Christoph Flamm, Universität Wien, AT Universität Wien Peter Stadler, Universität Leipzig, DE Walter Fontana, Harvard Medical School, MA Christian Reidys, University of Southern Denmark, Odense, DK Thomas Wiehe, Universität Köln, DE Martin Nowak, Harvard University, MA Stefan Bonhoeffer, ETH Zürich, CH Christian Forst, Southwestern Medcial Center, University of Texas, Dallas, TX Erich Bornberg-Bauer, Münster, DE

40 Acknowledgement of support Fonds zur Förderung der wissenschaftlichen Forschung (FWF) Projects No , 10578, 11065, , and Universität Wien Wiener Wissenschafts-, Forschungs- und Technologiefonds (WWTF) Project No. Mat05 Jubiläumsfonds der Österreichischen Nationalbank Project No. Nat-7813 European Commission: Contracts No , (NEST) Austrian Genome Research Program GEN-AU: Bioinformatics Network (BIN) Österreichische Akademie der Wissenschaften Siemens AG, Austria Universität Wien and the Santa Fe Institute

41 Thank you for your attention!

42 Web-Page for further information: Preprint: Santa Fe Institute Working Paper: #

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